The Peacekeeper Directorate - Functionally their principal military arm. Divided into four equal fleets with an astrographic area of responsibility.
The Public Safety Directorate - Operates as an exceptionally well armed interstellar law enforcement service with a very broad remit. Divided into a series of Precincts of varying size and astrographic responsibility.
The Science Directorate - Smallest of the three directorates, but potentially the one we are most likely to meet. Divided into Orders according to a wide variety of focal points.
We can say for sure that each of the Peacekeeper Fleets is anchored by a Sanctuary-class Fleet Tender, a tremendous five megaton mothership that supports an approximate dozen of short-range Corvettes. They are then supported by two older, much smaller, fleet tenders. The exact numbers of Corvettes in each fleet is not precisely known. Providing some heavy metal staying power, each fleet is also backed by a quartet of Liberators.
The Public Safety Directorate operates in, we believe, six Precincts, sharing a dozen of the older pattern fleet tenders which have been relegated to home service. In addition, they have a wide variety of older corvettes, and Alert-class public safety corvettes, almost like space-going law enforcement cruisers. A dozen Scientist-class cruisers and about a half-dozen older Solace-class battlecruisers help provide additional strength.
The Science Directorate is at least a dozen, but probably more, Scientist-class cruisers, and an equal number of Solace-class battlecruisers. The Solace-class, though a battlecruiser, is still a very capable research and diplomatic vessel, but a lot stronger in combat. Beware that outwardly they appear nearly identical, but you would not want to mistake the two.